Propensity Score Matching MOC

Matching and propensity-score methods identify causal effects under selection on observables: if treatment is independent of potential outcomes conditional on covariates (Ignorability) and every covariate profile has support in both arms (Overlap), then matched untreated units supply the treated counterfactual. The Propensity-Score is the workhorse — a one-dimensional balancing score that makes high-dimensional conditioning feasible. Crucially, the propensity score buys tractability, not identification: the design is only as credible as the untestable unconfoundedness assumption, which is why overlap diagnostics and sensitivity analysis are central.

Papers

Key Concepts

Ignorability (unconfoundedness / selection on observables) · Overlap (common support) · Propensity-Score (balancing score) · Causal-Estimand (ATT) · SUTVA · Potential-Outcomes

Debates & Contradictions

  • Does matching overcome the LaLonde critique? Dehejia–Wahba said largely yes; SmithTodd2005-ReconcilingPSMEvidence showed the result is specification- and sample-dependent. Cross-sectional matching cannot remove time-invariant unobservables; DiD-matching can.
  • Identification vs. implementation. The propensity score does not weaken unconfoundedness; much of the literature is about disciplining the many implementation choices that otherwise become researcher degrees of freedom.
  • Untestable core assumption. Because unconfoundedness cannot be tested directly, overlap diagnostics, placebo outcomes, and Rosenbaum bounds substitute for a formal test.

Next

PSM shares its selection-on-observables foundation with regression adjustment and the propensity-score DiD of Abadie2005-SemiparametricDiD in DiD; its potential-outcomes basis links to Foundations. Broader program-evaluation context: ImbensWooldridge2009-ProgramEvaluation.